Find the following probabilities for the standard normal random variable z (Keep in mind that the mean of the standard normal distribution is 0 and its standard deviation is 1). 1. P(z < 1.99) = (Round your answer to 4 decimal places) 2. P(z > -1.42) = (Round your answer to 4 decimal places)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![**Understanding Standard Normal Distribution: Calculating Probabilities**
Explore how to determine probabilities for a standard normal random variable \( z \). Recall that the mean of the standard normal distribution is 0 and its standard deviation is 1.
1. **Calculate \( P(z < 1.99) \):**
Determine the probability that \( z \) is less than 1.99.
*Round your answer to 4 decimal places.*
\[
P(z < 1.99) = \, \boxed{\, \, }
\]
2. **Calculate \( P(z > -1.42) \):**
Determine the probability that \( z \) is greater than -1.42.
*Round your answer to 4 decimal places.*
\[
P(z > -1.42) = \, \boxed{\, \, }
\]
Ensure you utilize the standard normal distribution table or a calculator to find these probabilities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa29210f1-c509-4cc5-a424-b61c622bd259%2Fcdbacf50-9d2c-418c-84c2-ddf97d30fdc3%2F39lupb_processed.png&w=3840&q=75)
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